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This research introduces Chain of Operators (CHOP), a framework that improves the generalization of frozen In-Context Operator Networks to out-of-distribution tasks without parameter updates. By chaining explicit elementary transformations with the base model, the method reduces inference error while maintaining interpretability and demonstrating cross-family generalization in partial differential equation solving. The approach effectively extends in-context learning principles from large language models to neural operator architectures, offering a promising path for adaptable scientific computing.
Harness In-Context Operator Learning with Chain of Operators
arXiv:2606.12318v1 Announce Type: new Abstract: Neural operators approximate mappings between function spaces, but often generalize poorly to other operators and usually require fine-tuning or retraining. In-Context Operator Networks (ICON) addresses this issue by prompting the model with numerical context so that the model learns specific operators from prompts and adapt to different operators without fine-tuning. However, ICON may still fail to generalize to out-of-distribution (OOD) operator tasks. Inpired by the success of harness engineering of Large Language models (LLMs), we introduce Chain of Operators (CHOP), a framework that harness a frozen ICON to OOD operator tasks without updating its parameters. Specifically, CHOP constructs a chain of operators consisting of explicit elementary transformations and the frozen ICON. Experiments on a scalar conservation law and a mean-field control problem show that CHOP reduces relative inference error over direct ICON evaluation, while each operator in the chain remains interpretable and in closed form. A chain constructed on one PDE family further generalizes to a different family, indicating shared mechanisms across harness systems.
Abstract:Neural operators approximate mappings between function spaces, but often generalize poorly to other operators and usually require fine-tuning or retraining. In-Context Operator Networks (ICON) addresses this issue by prompting the model with numerical context so that the model learns specific operators from prompts and adapt to different operators without fine-tuning. However, ICON may still fail to generalize to out-of-distribution (OOD) operator tasks. Inpired by the success of harness engineering of Large Language models (LLMs), we introduce Chain of Operators (CHOP), a framework that harness a frozen ICON to OOD operator tasks without updating its parameters. Specifically, CHOP constructs a chain of operators consisting of explicit elementary transformations and the frozen ICON. Experiments on a scalar conservation law and a mean-field control problem show that CHOP reduces relative inference error over direct ICON evaluation, while each operator in the chain remains interpretable and in closed form. A chain constructed on one PDE family further generalizes to a different family, indicating shared mechanisms across harness systems.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.12318 [cs.LG]
(or arXiv:2606.12318v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.12318 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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